Estimation of the predictive probability function of a negative binomial distribution is addressed under the Kullback—Leibler risk. An identity that relates Bayesian predictive probability estimation to Bayesian point estimation is derived. Such identities are known in the cases of normal and Poisson distributions, and the paper extends the result to the negative binomial case. By using the derived identity, a dominance property of a Bayesian predictive probability is studied when the parameter space is restricted.

中文翻译：

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负二项式模型的贝叶斯预测分布

负二项式分布的预测概率函数的估计在Kullback-Leibler风险下进行。导出将贝叶斯预测概率估计与贝叶斯点估计相关的身份。在正态分布和泊松分布的情况下，这样的身份是已知的，并且本文将结果扩展到负二项式情况。通过使用导出的身份，研究了参数空间受限时的贝叶斯预测概率的优势性质。